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Math Requirements for Theory

What math classes would you recommend a prospective student to take if their interested in theory (micro theory, game theory, decision theory, mechanism design, contract theory, etc.). I figured this post might help some people out.

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Re: Math Requirements for Theory

I've gathered these areas to be of immediate importance (aka you'll be using these) for doing work in game theory and mechanism design:

Analysis
Topology (very important)
Graph Theory
Combinatorics

I doubt that you'll actually need anything past analysis on your transcript, but I suppose more is preferred (as always). The areas highlighted are stuff that theorists ought to be familiar with since I've noticed its applications in numerous papers.

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Re: Math Requirements for Theory

Originally Posted by tutonic
I've gathered these areas to be of immediate importance (aka you'll be using these) for doing work in game theory and mechanism design:

Analysis
Topology

Graph Theory
Combinatorics

I doubt that you'll actually need anything past analysis on your transcript, but I suppose more is preferred (as always). The areas highlighted are stuff that theorists ought to be familiar with since I've noticed its applications in numerous papers.
The first two of these suggestions are good. Most basic results in point-set topology and analysis are useful in pretty much every sub-field of microeconomic theory.

Unless you know you are interested in networks, I think your time would be better spent in a rigorous probability or stochastic processes course (probability measures, definition of expectation, martingales, brownian motion, etc.). Dynamics and continuous-time methods are becoming fairly popular in applied theory. So, the chances that you use that material are much higher than something more niche, like graph theory or combinatorics.

If you are interested in decision theory, you will need analysis, topology, and probability theory. But you might also look into taking some form of advanced linear algebra, one that serves as an introduction to functional analysis (Banach spaces, Hilbert spaces, Riesz representation theorem, etc.).

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Re: Math Requirements for Theory

Originally Posted by Food4Thought
The first two of these suggestions are good. Most basic results in point-set topology and analysis are useful in pretty much every sub-field of microeconomic theory.

Unless you know you are interested in networks, I think your time would be better spent in a rigorous probability or stochastic processes course (probability measures, definition of expectation, martingales, brownian motion, etc.). Dynamics and continuous-time methods are becoming fairly popular in applied theory. So, the chances that you use that material are much higher than something more niche, like graph theory or combinatorics.

If you are interested in decision theory, you will need analysis, topology, and probability theory. But you might also look into taking some form of advanced linear algebra, one that serves as an introduction to functional analysis (Banach spaces, Hilbert spaces, Riesz representation theorem, etc.).
I concur that graph theory and combinatorics will only be pertinent if you're doing networks and informations.

Oh yeah, it totally escaped me. Measure Theory and measure theoretic probability will also be useful for games/mechanisms.

I could be mistaken but unless you're super clear on wanting to do theory - and applying to Top 10s where it is super competitive -, no school will actually expect you to have all these in your transcript. Most of these are pick-up-as-you-go kind of thing during your 5 year stay there.

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Re: Math Requirements for Theory

Theory isn't pick-up-as-you-go. If you want to do some kind of combined experimental + theory work, or "applied theory" in micro, then yes, you can pick up math as you go. But there are very few successful theory candidates who didn't take more pure math than econ as an undergraduate.

The line between theory candidates and non-theory candidates is very clear. Unless you have some kind of prior validation of your math ability like an IMO or Putnam award, it's generally not advisable to go into a program with the intention to specify in pure theory without at least 1 advanced course in each math field and several courses in and beyond measure theory.

Foreign applicants are an exception.

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Re: Math Requirements for Theory

Originally Posted by chateauheart
Theory isn't pick-up-as-you-go. If you want to do some kind of combined experimental + theory work, or "applied theory" in micro, then yes, you can pick up math as you go. But there are very few successful theory candidates who didn't take more pure math than econ as an undergraduate.

The line between theory candidates and non-theory candidates is very clear. Unless you have some kind of prior validation of your math ability like an IMO or Putnam award, it's generally not advisable to go into a program with the intention to specify in pure theory without at least 1 advanced course in each math field and several courses in and beyond measure theory.

Foreign applicants are an exception.
I did not know that. The way I saw it, one only requires analysis as a formal course and will be sufficiently equipped to self-learn and make up for all the shortfalls during the first 2 years of coursework (which is what I'm intending to do; I plan to start during the 2-3 months leading up to admission in the Fall, when I eventually apply).
What kind of courses are you referring to that subsume under beyond measure theory? Also, what do you mean by foreign applicants are an exception? Are we subscribed to relatively more lax requirements by adcoms?

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Re: Math Requirements for Theory

Let me add a piece to Chateauheart's advice. The market for pure theorists is very thin and dominated by a small number of schools. If you haven't done much math, you should be wary of committing yourself to pure theory.

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Re: Math Requirements for Theory

Originally Posted by startz
Let me add a piece to Chateauheart's advice. The market for pure theorists is very thin and dominated by a small number of schools. If you haven't done much math, you should be wary of committing yourself to pure theory.
What if, hypothetically, I can get into schools (USNEWS) ranked 15-25 - I'm currently eyeing Rochester but will be reaching for Wisconsin Madison - with the likes of Penn State being my safety. Is it then still worthwhile to pursue theory?

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Re: Math Requirements for Theory

I think that's risky, but there might be others here who can give a better answer. The other thing to remember is that lots of economists do some theory. It's the "pure theory" market that's particularly tough.

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Re: Math Requirements for Theory

Originally Posted by tutonic
I did not know that. The way I saw it, one only requires analysis as a formal course and will be sufficiently equipped to self-learn and make up for all the shortfalls during the first 2 years of coursework (which is what I'm intending to do; I plan to start during the 2-3 months leading up to admission in the Fall, when I eventually apply).
What kind of courses are you referring to that subsume under beyond measure theory? Also, what do you mean by foreign applicants are an exception? Are we subscribed to relatively more lax requirements by adcoms?
Most courses on measure theory really just teach you the basic tools. Most parts of advanced mathematics use these tools without even mentioning them so in that sense it is a very basic course in the grand scheme of things.

I took an analysis course once during my undergrad and this was the syllabus :

Banach and Hilbert spaces, theorems of Hahn-Banach and Banach-Steinhaus, open mapping theorem,closed graph theorem, Fredholm theory, spectral theorem for compact self-adjoint operators, spectral theorem for bounded selfadjointoperators. Additional topics to be chosen from: Lorentz spaces and interpolation, Banach algebras and the Gelfandtheory, distributions and Sobolev spaces, The von Neumann-Schatten classes, symbolic calculus of Hilbert space operators,representation theory and harmonic analysis, semigroups of operators, Krein-Milman theorem, tensor products of Hilbert spacesand Banach spaces, fixed point theorems.

I think what cheatuheart was getting at is that most theory applicants would have had several courses like the one above.